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<li><a class="reference internal" href="#">Plotting Learning Curves</a></li>
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  <div class="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-model-selection-plot-learning-curve-py"><span class="std std-ref">here</span></a> to download the full example code or to run this example in your browser via Binder</p>
</div>
<div class="sphx-glr-example-title section" id="plotting-learning-curves">
<span id="sphx-glr-auto-examples-model-selection-plot-learning-curve-py"></span><h1>Plotting Learning Curves<a class="headerlink" href="#plotting-learning-curves" title="Permalink to this headline">¶</a></h1>
<p>In the first column, first row the learning curve of a naive Bayes classifier
is shown for the digits dataset. Note that the training score and the
cross-validation score are both not very good at the end. However, the shape
of the curve can be found in more complex datasets very often: the training
score is very high at the beginning and decreases and the cross-validation
score is very low at the beginning and increases. In the second column, first
row we see the learning curve of an SVM with RBF kernel. We can see clearly
that the training score is still around the maximum and the validation score
could be increased with more training samples. The plots in the second row
show the times required by the models to train with various sizes of training
dataset. The plots in the third row show how much time was required to train
the models for each training sizes.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>

<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn.naive_bayes</span> <span class="kn">import</span> <span class="n">GaussianNB</span>
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <span class="n">SVC</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">load_digits</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">learning_curve</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">ShuffleSplit</span>


<span class="k">def</span> <span class="nf">plot_learning_curve</span><span class="p">(</span><span class="n">estimator</span><span class="p">,</span> <span class="n">title</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">axes</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">ylim</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
                        <span class="n">n_jobs</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">train_sizes</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mi">5</span><span class="p">)):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Generate 3 plots: the test and training learning curve, the training</span>
<span class="sd">    samples vs fit times curve, the fit times vs score curve.</span>

<span class="sd">    Parameters</span>
<span class="sd">    ----------</span>
<span class="sd">    estimator : object type that implements the &quot;fit&quot; and &quot;predict&quot; methods</span>
<span class="sd">        An object of that type which is cloned for each validation.</span>

<span class="sd">    title : string</span>
<span class="sd">        Title for the chart.</span>

<span class="sd">    X : array-like, shape (n_samples, n_features)</span>
<span class="sd">        Training vector, where n_samples is the number of samples and</span>
<span class="sd">        n_features is the number of features.</span>

<span class="sd">    y : array-like, shape (n_samples) or (n_samples, n_features), optional</span>
<span class="sd">        Target relative to X for classification or regression;</span>
<span class="sd">        None for unsupervised learning.</span>

<span class="sd">    axes : array of 3 axes, optional (default=None)</span>
<span class="sd">        Axes to use for plotting the curves.</span>

<span class="sd">    ylim : tuple, shape (ymin, ymax), optional</span>
<span class="sd">        Defines minimum and maximum yvalues plotted.</span>

<span class="sd">    cv : int, cross-validation generator or an iterable, optional</span>
<span class="sd">        Determines the cross-validation splitting strategy.</span>
<span class="sd">        Possible inputs for cv are:</span>
<span class="sd">          - None, to use the default 5-fold cross-validation,</span>
<span class="sd">          - integer, to specify the number of folds.</span>
<span class="sd">          - :term:`CV splitter`,</span>
<span class="sd">          - An iterable yielding (train, test) splits as arrays of indices.</span>

<span class="sd">        For integer/None inputs, if ``y`` is binary or multiclass,</span>
<span class="sd">        :class:`StratifiedKFold` used. If the estimator is not a classifier</span>
<span class="sd">        or if ``y`` is neither binary nor multiclass, :class:`KFold` is used.</span>

<span class="sd">        Refer :ref:`User Guide &lt;cross_validation&gt;` for the various</span>
<span class="sd">        cross-validators that can be used here.</span>

<span class="sd">    n_jobs : int or None, optional (default=None)</span>
<span class="sd">        Number of jobs to run in parallel.</span>
<span class="sd">        ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.</span>
<span class="sd">        ``-1`` means using all processors. See :term:`Glossary &lt;n_jobs&gt;`</span>
<span class="sd">        for more details.</span>

<span class="sd">    train_sizes : array-like, shape (n_ticks,), dtype float or int</span>
<span class="sd">        Relative or absolute numbers of training examples that will be used to</span>
<span class="sd">        generate the learning curve. If the dtype is float, it is regarded as a</span>
<span class="sd">        fraction of the maximum size of the training set (that is determined</span>
<span class="sd">        by the selected validation method), i.e. it has to be within (0, 1].</span>
<span class="sd">        Otherwise it is interpreted as absolute sizes of the training sets.</span>
<span class="sd">        Note that for classification the number of samples usually have to</span>
<span class="sd">        be big enough to contain at least one sample from each class.</span>
<span class="sd">        (default: np.linspace(0.1, 1.0, 5))</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">if</span> <span class="n">axes</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
        <span class="n">_</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>

    <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
    <span class="k">if</span> <span class="n">ylim</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
        <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="o">*</span><span class="n">ylim</span><span class="p">)</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Training examples&quot;</span><span class="p">)</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Score&quot;</span><span class="p">)</span>

    <span class="n">train_sizes</span><span class="p">,</span> <span class="n">train_scores</span><span class="p">,</span> <span class="n">test_scores</span><span class="p">,</span> <span class="n">fit_times</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> \
        <span class="n">learning_curve</span><span class="p">(</span><span class="n">estimator</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="n">cv</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=</span><span class="n">n_jobs</span><span class="p">,</span>
                       <span class="n">train_sizes</span><span class="o">=</span><span class="n">train_sizes</span><span class="p">,</span>
                       <span class="n">return_times</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
    <span class="n">train_scores_mean</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">train_scores</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
    <span class="n">train_scores_std</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">train_scores</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
    <span class="n">test_scores_mean</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">test_scores</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
    <span class="n">test_scores_std</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">test_scores</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
    <span class="n">fit_times_mean</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">fit_times</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
    <span class="n">fit_times_std</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">fit_times</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>

    <span class="c1"># Plot learning curve</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">grid</span><span class="p">()</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="n">train_sizes</span><span class="p">,</span> <span class="n">train_scores_mean</span> <span class="o">-</span> <span class="n">train_scores_std</span><span class="p">,</span>
                         <span class="n">train_scores_mean</span> <span class="o">+</span> <span class="n">train_scores_std</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span>
                         <span class="n">color</span><span class="o">=</span><span class="s2">&quot;r&quot;</span><span class="p">)</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="n">train_sizes</span><span class="p">,</span> <span class="n">test_scores_mean</span> <span class="o">-</span> <span class="n">test_scores_std</span><span class="p">,</span>
                         <span class="n">test_scores_mean</span> <span class="o">+</span> <span class="n">test_scores_std</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span>
                         <span class="n">color</span><span class="o">=</span><span class="s2">&quot;g&quot;</span><span class="p">)</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">train_sizes</span><span class="p">,</span> <span class="n">train_scores_mean</span><span class="p">,</span> <span class="s1">&#39;o-&#39;</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">&quot;r&quot;</span><span class="p">,</span>
                 <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Training score&quot;</span><span class="p">)</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">train_sizes</span><span class="p">,</span> <span class="n">test_scores_mean</span><span class="p">,</span> <span class="s1">&#39;o-&#39;</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">&quot;g&quot;</span><span class="p">,</span>
                 <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Cross-validation score&quot;</span><span class="p">)</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s2">&quot;best&quot;</span><span class="p">)</span>

    <span class="c1"># Plot n_samples vs fit_times</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">grid</span><span class="p">()</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">train_sizes</span><span class="p">,</span> <span class="n">fit_times_mean</span><span class="p">,</span> <span class="s1">&#39;o-&#39;</span><span class="p">)</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="n">train_sizes</span><span class="p">,</span> <span class="n">fit_times_mean</span> <span class="o">-</span> <span class="n">fit_times_std</span><span class="p">,</span>
                         <span class="n">fit_times_mean</span> <span class="o">+</span> <span class="n">fit_times_std</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Training examples&quot;</span><span class="p">)</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;fit_times&quot;</span><span class="p">)</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;Scalability of the model&quot;</span><span class="p">)</span>

    <span class="c1"># Plot fit_time vs score</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">grid</span><span class="p">()</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">fit_times_mean</span><span class="p">,</span> <span class="n">test_scores_mean</span><span class="p">,</span> <span class="s1">&#39;o-&#39;</span><span class="p">)</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="n">fit_times_mean</span><span class="p">,</span> <span class="n">test_scores_mean</span> <span class="o">-</span> <span class="n">test_scores_std</span><span class="p">,</span>
                         <span class="n">test_scores_mean</span> <span class="o">+</span> <span class="n">test_scores_std</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;fit_times&quot;</span><span class="p">)</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Score&quot;</span><span class="p">)</span>
    <span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;Performance of the model&quot;</span><span class="p">)</span>

    <span class="k">return</span> <span class="n">plt</span>


<span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">15</span><span class="p">))</span>

<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">load_digits</span><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>

<span class="n">title</span> <span class="o">=</span> <span class="s2">&quot;Learning Curves (Naive Bayes)&quot;</span>
<span class="c1"># Cross validation with 100 iterations to get smoother mean test and train</span>
<span class="c1"># score curves, each time with 20% data randomly selected as a validation set.</span>
<span class="n">cv</span> <span class="o">=</span> <span class="n">ShuffleSplit</span><span class="p">(</span><span class="n">n_splits</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>

<span class="n">estimator</span> <span class="o">=</span> <span class="n">GaussianNB</span><span class="p">()</span>
<span class="n">plot_learning_curve</span><span class="p">(</span><span class="n">estimator</span><span class="p">,</span> <span class="n">title</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">axes</span><span class="o">=</span><span class="n">axes</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">ylim</span><span class="o">=</span><span class="p">(</span><span class="mf">0.7</span><span class="p">,</span> <span class="mf">1.01</span><span class="p">),</span>
                    <span class="n">cv</span><span class="o">=</span><span class="n">cv</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span>

<span class="n">title</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">&quot;Learning Curves (SVM, RBF kernel, $\gamma=0.001$)&quot;</span>
<span class="c1"># SVC is more expensive so we do a lower number of CV iterations:</span>
<span class="n">cv</span> <span class="o">=</span> <span class="n">ShuffleSplit</span><span class="p">(</span><span class="n">n_splits</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">estimator</span> <span class="o">=</span> <span class="n">SVC</span><span class="p">(</span><span class="n">gamma</span><span class="o">=</span><span class="mf">0.001</span><span class="p">)</span>
<span class="n">plot_learning_curve</span><span class="p">(</span><span class="n">estimator</span><span class="p">,</span> <span class="n">title</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">axes</span><span class="o">=</span><span class="n">axes</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">ylim</span><span class="o">=</span><span class="p">(</span><span class="mf">0.7</span><span class="p">,</span> <span class="mf">1.01</span><span class="p">),</span>
                    <span class="n">cv</span><span class="o">=</span><span class="n">cv</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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